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Technique of checking missed eigenvalues for eigenproblem with damping matrix
Author(s) -
Jung HyungJo,
Kim DongHyawn,
Lee InWon
Publication year - 2000
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/1097-0207(20010110)50:1<55::aid-nme21>3.0.co;2-v
Subject(s) - eigenvalues and eigenvectors , damping matrix , lanczos resampling , subspace topology , mathematics , matrix (chemical analysis) , sequence (biology) , matrix differential equation , mathematical analysis , stiffness matrix , structural engineering , stiffness , engineering , physics , materials science , quantum mechanics , composite material , biology , genetics
In the case of the non‐proportionally damped system such as the soil–structure interaction system, the structural control system and composite structures, the eigenproblem with the damping matrix should be necessarily performed to obtain the exact dynamic response. However, most of the eigenvalue analysis methods such as the subspace iteration method and the Lanczos method may miss some eigenvalues in the required ones. Therefore, the eigenvalue analysis method must include a technique to check the missed eigenvalues to become the practical tools. In the case of the undamped or proportionally damped system the missed eigenvalues can easily be checked by using the well‐known Sturm sequence property, while in the case of the non‐proportionally damped system a checking technique has not been developed yet. In this paper, a technique of checking the missed eigenvalues for the eigenproblem with the damping matrix is proposed by applying the argument principle. To verify the effectiveness of the proposed method, two numerical examples are considered. Copyright © 2001 John Wiley & Sons, Ltd.